Let's say I place four thermosensors on my body. Then, on top of these thermosensors I place four different items (A, B, C, and D). All four items start out at the same (rather cold) temperature. However, items A and B have the same specific heat, but different thermal conductivities, while C and D have the same thermal conductivity but their specific heats are different.

This is what I think will happen (I'm hoping someone with more physics knowledge can confirm or debunk this): when I place items A and B on my body one will feel colder than the other (because its thermal conductivity is higher), however, the thermosensor will tell me that their temperatures are the same, and not only that, but that the rates at which their temperatures rise (due to contact with my body) will also be the same, thus the two items will (in theory) remain at the same temperature until they both reach equilibrium with my body temp (in other words their temperatures will change "in unison", though it may not feel that way). Meanwhile, when I place items C and D on my body they will feel like they're the same temperature (because they are, and because they have the same thermal conductivity) However, one will warm up faster than the other, reaching equilibrium with my body temperature sooner, because it has a lower specific heat (again, this may not seem to correspond with what I'm feeling).
If my little theory is wrong, then what, in fact, are the relationships between A and B, and C and D, both in terms of how they FEEL and in terms of what the thermosensor will say about them? How would the experiment be affected if all four items started out hot rather than cold (it seems to me that then the specific heat of my own body comes into play, is this so? Does it come into play if the items are cold as well?).
Finally, what are some safe substances (liquids or powder/gravel type items that could be placed in flexible plastic tubes) that change temperature at a noticeably different rate from water? (either in terms of how they feel or in terms of real temp. change, I'm ideally looking for something from each category for maximum variety).

You will feel the same thing as what the thermal sensor will show, because both measure the same thing, slight gradient across skin notwithstanding.

The objects A and B will not feel like they have the same temperature. The body with low thermal conductivity will quickly warm up on the surface, staying cold on the inside. The body with higher conductivity will keep taking away heat from your body until the center warms through, and only then will start feeling warmer on the surface. Compare something like piece of marble to piece of aluminum. Aluminum will feel colder than marble for that very reason. Their heat capacities are actually pretty close.

For bodies C and D, the difference will actually depend on your body's own ability to carry in heat. If heat conductivity of your body is much higher than that of C and D, they'll appear to have the same temperature, even if heat capacities are very different.

If your body conduct's heat worse than C and D, then the one with higher heat capacity will take longer to warm through, and so will feel cold significantly longer.